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Simplifying (2x + -3)(x + 4) = 621 Reorder the terms: (-3 + 2x)(x + 4) = 621 Reorder the terms: (-3 + 2x)(4 + x) = 621 Multiply (-3 + 2x) * (4 + x) (-3(4 + x) + 2x * (4 + x)) = 621 ((4 * -3 + x * -3) + 2x * (4 + x)) = 621 ((-12 + -3x) + 2x * (4 + x)) = 621 (-12 + -3x + (4 * 2x + x * 2x)) = 621 (-12 + -3x + (8x + 2x2)) = 621 Combine like terms: -3x + 8x = 5x (-12 + 5x + 2x2) = 621 Solving -12 + 5x + 2x2 = 621 Solving for variable 'x'. Reorder the terms: -12 + -621 + 5x + 2x2 = 621 + -621 Combine like terms: -12 + -621 = -633 -633 + 5x + 2x2 = 621 + -621 Combine like terms: 621 + -621 = 0 -633 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -316.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '316.5' to each side of the equation. -316.5 + 2.5x + 316.5 + x2 = 0 + 316.5 Reorder the terms: -316.5 + 316.5 + 2.5x + x2 = 0 + 316.5 Combine like terms: -316.5 + 316.5 = 0.0 0.0 + 2.5x + x2 = 0 + 316.5 2.5x + x2 = 0 + 316.5 Combine like terms: 0 + 316.5 = 316.5 2.5x + x2 = 316.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 316.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 316.5 + 1.5625 Combine like terms: 316.5 + 1.5625 = 318.0625 1.5625 + 2.5x + x2 = 318.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 318.0625 Calculate the square root of the right side: 17.834306827 Break this problem into two subproblems by setting (x + 1.25) equal to 17.834306827 and -17.834306827.Subproblem 1
x + 1.25 = 17.834306827 Simplifying x + 1.25 = 17.834306827 Reorder the terms: 1.25 + x = 17.834306827 Solving 1.25 + x = 17.834306827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 17.834306827 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 17.834306827 + -1.25 x = 17.834306827 + -1.25 Combine like terms: 17.834306827 + -1.25 = 16.584306827 x = 16.584306827 Simplifying x = 16.584306827Subproblem 2
x + 1.25 = -17.834306827 Simplifying x + 1.25 = -17.834306827 Reorder the terms: 1.25 + x = -17.834306827 Solving 1.25 + x = -17.834306827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -17.834306827 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -17.834306827 + -1.25 x = -17.834306827 + -1.25 Combine like terms: -17.834306827 + -1.25 = -19.084306827 x = -19.084306827 Simplifying x = -19.084306827Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.584306827, -19.084306827}
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